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Step2247 [10]
2 years ago
11

It takes at 45 minutes to complete his science homework. It takes him 2/3 as long to complete his math homework. How long does i

t take add to complete his math homework?
Mathematics
2 answers:
lidiya [134]2 years ago
6 0
The person above me is right
Llana [10]2 years ago
5 0

Answer:

30 minutes

Step-by-step explanation:

45 =     15 +15 +15     (3 parts of 15)

2 parts of 15  = 30

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A 12-member jury is to be selected from 15 men and 13 women. Find the probability that this jury has 6 or 7 males.
Bas_tet [7]

Answer:

The right solution is "0.5545".

Step-by-step explanation:

According to the question,

The probability of having 6 or 7 males will be:

= P(6 \ males)+ P(7 \ males)

= \frac{15_C_6\times 13_C_6}{28_C_{12}} + \frac{15_C_7\times 13_C_5}{28_C_{12}}

= \frac{5005\times 1716+6435\times 1287}{30421755}

= \frac{16870425}{30421755}

= 0.5545

8 0
2 years ago
Which is an example of perpendicular lines?
lara31 [8.8K]
The answer would be choice C. 
Perpendicular lines cross each other and form a right angle as you can see marked in the third picture.
8 0
3 years ago
Read 2 more answers
Mrs.smith earns $3500 a month. She saves $280 a month. Savings is what percent of her income?
arlik [135]

Answer:

3500 280

Step-by-step explanation:

280/3500

280 divided by 3500 times 100 (type this into a calculator)

its 8 her savings are 8 percent of her income

4 0
3 years ago
Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation
Gemiola [76]

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

a=b=c=0,p=5

That is, the equation of the sphere in cartesian coordinates is,

(x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}

\Rightarrow x^{2}+y^{2}+z^{2}=25

Now, the cylindrical coordinate system is represented by (r, \theta,z)

The relation between cartesian and cylindrical coordinates is given by,

x=rcos\theta,y=rsin\theta,z=z

r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

r^{2}+z^{2}=25

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

(x-a)^{2}+(y-b)^{2}=p^{2}

Here, it is given that the center is at origin & radius is 1. That is, here, we have, a=b=0,p=1. Then the equation of the cylinder in cartesian coordinates is,

x^{2}+y^{2}=1

Now, the spherical coordinate system is represented by (\rho,\theta,\phi)

The relation between cartesian and spherical coordinates is given by,

x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

(\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1

\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1

\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1

\Rightarrow \rho^{2} sin^{2}\phi=1 (As sin^{2}\theta+cos^{2}\theta=1)

Note that \rho represents the distance of a point from the origin, which is always positive. \phi represents the angle made by the line segment joining the point with z-axis. The range of \phi is given as 0\leq \phi\leq \pi. We know that in this range the sine function is positive. Thus, we can say that sin\phi is always positive.

Thus, we can square root both sides and only consider the positive root as,

\Rightarrow \rho sin\phi=1

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is r^{2}+z^{2}=25

(b) The equation of the given cylinder in spherical coordinates is \rho sin\phi=1

7 0
3 years ago
In fig if x+y=w+z then prove that AOB is a line.​
frez [133]

Answer:

As Given, x+y=w+z

To Prove: AOB is a line or x+y=180

∘

(linear pair.)

According to the question,

x+y+w+z=360

∘

∣ Angles around a point.

(x+y)+(w+z)=360

∘

(x+y)+(x+y)=360

∘

∣ Given x+y=w+z

2(x+y)=360

∘

(x+y)=180

∘

Hence, x+y makes a linear pair.

Therefore, AOB is a straight line

4 0
3 years ago
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